e-Day

[Dieter]

(07-03-2018 11:53 AM)Pjwum Wrote:  Regarding my little program to find n for 2.718 there are interesting forensic effects. In fact, the numerical solver delivers another n. Graphing (1+1/n)^n and zooming around 4822.55 a pronounced sawtooth alternates above and below eday.

Of course the is no such sawtooth, mathematically. What you see is the result of roundoff errors, especially when calculating 1+1/n. After the addition of 1 only 8 out of 12 digits of the original 1/n value are left. Maybe you can try rewriting the equation as exp[n · ln1+x(1/n)].

BTW the exact result is  n = 4821,66555538...

Dieter